{ "metadata": { "name": "", "signature": "sha256:881432a5cd98267b92bdfa11e021925fdef61ae98abdadccafbf254c6f9ca038" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "12: Band theory of solids" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 12.1, Page number 243" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "EF=8; #fermi energy(eV)\n", "e=1.6*10**-19; #conversion factor from J to eV\n", "m=9.1*10**-31; #mass of electron(kg)\n", "\n", "#Calculation\n", "E0bar=3*EF/5; \n", "v=math.sqrt(2*E0bar*e/m); #speed of electron(m/s)\n", "\n", "#Result\n", "print \"speed of electron is\",round(v/10**6,1),\"*10**6 m/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "speed of electron is 1.3 *10**6 m/s\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 12.2, Page number 244" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "I=8; #current(ampere)\n", "r=9*10**-4; #radius(m)\n", "V=5; #potential difference(V)\n", "L=1; #length(m)\n", "\n", "#Calculation\n", "A=math.pi*r**2; #area of wire(m**2)\n", "E=V/L;\n", "J=I/A; #current density(V/m)\n", "rho=E/J; #resistivity(ohm m)\n", "\n", "#Result\n", "print \"current density is\",round(J/10**6,3),\"*10**6 V/m\"\n", "print \"resistivity is\",round(rho*10**6,2),\"*10**-6 ohm m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "current density is 3.144 *10**6 V/m\n", "resistivity is 1.59 *10**-6 ohm m\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 12.3, Page number 245" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "n=1;\n", "a=4*10**-10; #lattice parameter(m)\n", "N=1.56*10**28; \n", "e=1.6*10**-19; #conversion factor from J to eV\n", "tow=10**-15; #collision time(s)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "\n", "#Calculation\n", "N=n/(a**3); #number of electrons per unit volume(per m**3)\n", "sigma=N*e**2*tow/m; #conductivity(per ohm m)\n", "rho=1/sigma; #resistivity(ohm m)\n", "\n", "#Result\n", "print \"conductivity is\",round(sigma/10**6,2),\"*10**6 ohm m\"\n", "print \"resistivity is\",rho,\"ohm m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "conductivity is 0.44 *10**6 ohm m\n", "resistivity is 2.275e-06 ohm m\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 12.4, Page number 247" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "k=1.38*10**-23; #boltzmann constant(J/K)\n", "NA=6.02*10**26; #avagadro number(k/mole)\n", "T=300; #temperature(K)\n", "EF=2; #fermi energy(eV)\n", "e=1.6*10**-19; #conversion factor from J to eV\n", "\n", "#Calculation\n", "C=math.pi**2*k**2*NA*T/(2*EF*e); #electronic specific heat(J/kmol/K)\n", "\n", "#Result\n", "print \"electronic specific heat is\",int(C),\"J/kmol/K\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "electronic specific heat is 530 J/kmol/K\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 12.5, Page number 247" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "K=327; #thermal conductivity(W/mK)\n", "T=300; #temperature(K)\n", "rho=7.13*10**3; #density(kg/m**3)\n", "NA=6.02*10**26; #avagadro number(k/mole)\n", "w=65.38; #atomic weight\n", "e=1.6*10**-19; #conversion factor from J to eV\n", "tow=2.5*10**-14; #relaxation time(s)\n", "m=9.1*10**-31; #mass of electron(kg)\n", "\n", "#Calculation\n", "N=2*rho*NA/w; #number of electrons per unit volume(per m**3)\n", "sigma=N*e**2*tow/m; #conductivity(per ohm m)\n", "L=K/(sigma*T); #lorentz number(W ohm/K**2)\n", "\n", "#Result\n", "print \"lorentz number is\",round(L*10**8,4),\"*10**-8 W ohm/K**2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "lorentz number is 1.1804 *10**-8 W ohm/K**2\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example number 12.6, Page number 248" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "e=1.6*10**-19; #conversion factor from J to eV\n", "n=5*10**28; #number of atoms(/m**3)\n", "\n", "#Calculation\n", "RH=-1/(n*e); #hall coefficient(m**3/C)\n", "\n", "#Result\n", "print \"hall coefficient is\",round(RH*10**9,3),\"*10**-9 m**3/C\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "hall coefficient is -0.125 *10**-9 m**3/C\n" ] } ], "prompt_number": 14 } ], "metadata": {} } ] }